Question

已知曲线C的参数方程为 x＝2cost y＝2sint（t为参数）,曲线C在点（...

已知曲线C的参数方程为 x＝2cost y＝2sint（t为参数）,曲线C在点（1, 3）处的切线为l,以坐标原点为极点,x轴的正半轴为极轴建立极坐标系,求l的极坐标方程．

Answer 1

x²
+
y²
=
2(cos²t
+
sin²t)
=
2曲线C为以(0,0)为圆心,半径为√2的圆.A(1,1),OA的斜率为1,切线l斜率为-1(与x轴的正半轴夹角为3π/4),方程为y
-
1
=
-(x
-
1),y
=
2
-
xl与x轴交于B(2,0)在l上任取一点M(ρ,θ)OM
=
ρ,OB
=
2,∠BOM
=
θ,∠MBO
=
π
-
3π/4
=
π/4,∠BMO
=
3π/4
-
θ按正弦定理:OM/sin∠MBO
=
OB/sin∠BMOρ/sin(π/4)
=
2/sin(3π/4
-
θ)ρ
=
√2/sin(3π/4
-
θ)以上回答你满意么?